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Structural and Navigational Analysis of Hypermedia Courseware

Chuen-Tsai Sun, Member, IEEE, Chien Chou, Member, IEEE, and Bing-Kuen Lin

Abstract - In addition to providing flexible access to instructional information and supporting convenient learning styles, educational hypermedia offers a non-sequential information presentation that markedly differs from conventional instructional systems. Many pedagogical issues are attributed to the non-linear structures of educational hypermedia systems. Consequently, an ideal educational hypermedia system should provide navigation guidance, knowledge construction assistance, and courseware analysis tools. By emphasizing courseware structure and navigational behavior in an educational hypermedia environment, this work presents several algorithmic analytical models of ideal educational hypermedia systems.

Three graph algorithms are educational hypermedia analysis are used to identify courseware structures: Minimum Cut-Set, Strongly Connected Components, and Cut Vertex. The algorithms allow us to construct a knowledge hierarchy, analyze a courseware network to determine whether it is well-structured, and automatically generate a hierarchical guidance map to help users navigate in a hypermedia environment. This work also provides two quantitative measures. Hyper Degree and Hyper Distance, to further describe navigational behavior in hypermedia environments. After performing instructional experiments, the above methods were applied to the accumulated data. 

I. Introduction

As the World Wide Web (WWW) evolves into an important instructional platform, educational hypermedia is gaining increasing attention. Hypermedia is made up of nodes that can contain text, graphics, audio, video, even entire programs, and is an open system that allows users to read from, append or write materials to shared structures. Consequently, educational hypermedia provides flexible means of accessing instructional information and supports various learning styles, thus accounting for its extensive use in computer-assisted learning systems.

From an instructional perspective, a critical feature of hypermedia should be carefully considered: it provides a non-sequential information presentation that differs markedly from the text-based material used in conventional instructional systems. Students learning hypermedia courseware, as described in [1], can determine what course nodes they go to at any time. However, sound structures and learning guidance are just as important as navigational freedom. A hypermedia learning system must be able to assist students in determining their performance and reading levels. Furthermore, an intelligent learning environment is expected to employ students' profile information in dynamically planning their courseware [2]. The success of this facility depends on thorough understanding of students' navigational patterns. Such a system should also effectively respond to a specific student's circumstances. For example, students jumping back and forth between concept groups in courseware may be the result of too many subordinate hyper-links being provided to beginners. In such cases, less relevant paths should be blocked temporarily, so that students can concentrate on more fundamental connections between concepts. Apparently, these functions are as necessary to further understanding of courseware structures as knowing students' navigational behaviors.

It is generally accepted that semantic networks in the human mind have underlying hierarchical structures resembling trees. Teachers represent their knowledge in hierarchical structures and store the knowledge in hypermedia courseware for students to retrieve more or less as recorded. Thus, hypertext projection profoundly influences teaching [3]. Moreover, hierarchical structures can help students organize their own knowledge [4]. Vassileva [5] introduced student modeling along three dimensions: levels of knowledge represented in the model, updating, and organization. In the third dimension, hierarchical belief structures are highly useful. That is, a hierarchical learning environment helps students not only during non-sequential information searches and browsing, but also during knowledge construction and integration. In both cases, complete understanding of hypermedia structures and navigation patterns is essential. When hypermedia courseware is massively constructed in an automatic manner, as described in [6], structural analysis becomes crucial.

Although hypermedia makes learning and information retrieval easier than printed texts, according to Conklin [7], it is also associated with disorientation and cognitive overheads which are in fact inter-related. Cognitive overhead is the additional mental effort users must make in order to choose which links from a large number of optional choices to follow and which to abandon. Not knowing one's location and a need for continual decision-making can be distracting and can complicate learning journeys in hypertext environments. Disorientation or "getting lost in hyperspace" results from not knowing one's location in hyperspace. Stanton, Taylor & Tweedie [8] suggested that users feel lost if they do not know their locations, where they came from, where they should go next, and how to get there.

Considerable interest has recently been focused on developing better navigational guidance tools to help users search and read to alleviate these problem. Among the proposed navigational guidance tools are Maps, Path, and History List. In a previous study, we showed navigational maps based on a hierarchical structure can help students learn more efficiently. Thus, in this study, we present a design for a hierarchical map to help users learn in hypermedia environments.

Students become disoriented in the structures of some hypermedia courseware because too many navigational choices are presented. After navigating for a while, orienting themselves in hyperspace and aiming for goal nodes become difficult. To make matters worse, some course nodes cannot be easily read and understood because courseware links have been arbitrarily added and not appropriately structured. Cognitive overhead usually occurs when a student needs to remember the relationships implied by the links between nodes in addition to understanding the content of the nodes. Moreover, when various navigational tools are provided for students to choose from, they may inadvertently make the overhead even heavier. That is, introducing hypermedia courseware brings up courseware navigation issues, as well as courseware construction issues.

The analytical results presented herein detail our efforts to construct a hypermedia instructional design methodology, as described in [9].

1. To assist teachers in developing well-structured hypermedia courseware.

(a) detecting inadequate courseware structures, then suggesting ways to improve them.

(b) determining how students navigate in the courseware and modifying students' profiles.

2. To assist students in reading hypermedia courseware and reducing the likelihood of missed nodes and cognitive overloading.

(a) supporting the development of navigational guidance tools.

(b) dynamically adjusting the information presented to students.

(c) assisting students in constructing their own knowledge structures.

These results will be used in a pedagogical design strategy and courseware writing project, which will be implemented in the CORAL (COoperative Remotely Accessible Learning) system [10]. These results can also used to extend previous research. For instance, Horney [11]) identified five separate navigational patterns in courseware, including Linear Traversal, Star, Extended Star, Side Trip, and Chaotic. We believe that these algorithms can be used to identify the rationales behind some of these patterns. Previous research also motivated us to study the concept of hyperness (non-linearity) in terms of hypermedia navigation. A conventional textbook is considered a linear presentation. If a student tends to navigate a hypermedia document according to a presumed order, his or her behavior is relatively linear, or less "hyper" than that of a classmate who explores the courseware in a spontaneous jump-around manner. This approach may help clarify student behaviors in network-based hypermedia learning systems.

The rest of this paper is organized as follows. Section II introduces the concept of hierarchical courseware structures. The graphic algorithms used herein to analyze courseware networks are also described. Section III presents Hyper Degree and Hyper Distance for measuring the hyperness of navigating in hypermedia. Section IV describes the instructional experiments and discusses the analytical results. Concluding remarks are given in Section V.

II. Identifying Courseware Structure

As mentioned above, maps based on hierarchical structures can help students navigate in courseware networks and acquire their knowledge. A hypermedia environment is typically a dynamic system in which course-nodes are constantly appended and updated. Consequently, maintaining a hierarchical structure, even if one is provided by the authors in the first place, is generally difficult. This explains why we feel it necessary to present algorithms that can automatically construct hierarchical maps of educational hypermedia courseware and dynamically adjust it later on.

Our results confirm not only that hypermedia structures can be represented as directed graphs, but also that graph algorithms can be used for effective analysis of hypermedia structures. In this study, we use three graph algorithms to analyze hypermedia courseware structures: Minimum Cut-Set, Strongly Connected Components, and Cut Vertex. The following briefly explains the algorithms and their use with educational hypermedia.

A. Minimum Cut-Set

Assume that two groups of nodes are linked by only one path, or very few paths. Students who miss such paths after reading through one group will also miss the information in the other group. We use the Minimum Cut-Set algorithm to examine this structural problem. A minimum cut-set in a connected graph is a minimal set of paths whose removal from the graph leaves the graph disconnected. For instance, as Fig. 1 depicts, we have two minimum cut-sets: {1, 2} and {6, 7}.

Fig. 1. Hyper-structure analysis using the Minimum Cut-Set algorithm. After removing two minimum cut-sets {1,2} and {6,7}, we obtain three isolated components.

Employing this algorithm to examine the structure of a courseware network initially involves finding minimum cut-sets in given courseware networks and then removing their members. After the cut sets are removed, by definition, the courseware network becomes separate components; each of which is then considered a basic unit of courseware. As Fig. 1 depicts, three components are left after removal of the two cut-sets. We then use the same algorithm to identify and remove minimum cut-sets within these connected components. The above steps are repeated until only one node exists in each component. Finally, a hierarchical courseware structure is obtained. Fig. 2 schematically depicts the hierarchy derived from to the structure in Fig. 1.

Fig. 2. Hierarchy derived from the structure in Fig. 1 after employing the Minimum Cut-Set algorithm.


As mentioned above, this method can easily construct hierarchical structures, however, it is limited in that it only considers numbers of paths, but not link directions in the courseware network. Link directions obviously contain pertinent information required for navigation, which is why we proceeded to apply the algorithm described below.

B. Strongly Connected Components

In undirected connected graphs, every node can be reached from every node. However, hypermedia courseware naturally forms directed graphs. Students can frequently avoid reading all nodes in a hypermedia course if they never backtrack to previously read nodes. In some cases, some nodes cannot be reached from the starting node of the courseware. Thus, directed-graph analysis is a prerequisite for studying hypermedia courseware. Below, we introduce directed-graph-based algorithm, Strongly Connected Components, for analyzing the hypermedia networks.

A directed graph is called strongly connected if every node can be reached from every other node. One can navigate in strongly connected graphs and visit every node without any backtracking. Employing the strongly connected algorithm to analyze a courseware network initially entails deriving strongly connected subgraphs, or components, in the courseware. A courseware network normally consists of several components, each a strongly connected subgraph that is considered a basic unit of the courseware. Hence, hierarchical courseware structures consisting of strongly connected components can be obtained. However, by definition, a strongly connected graph cannot be further divided into smaller components. Therefore, two-level courseware structures are always obtained. Fig. 3 and Fig. 4 display, respectively, the components and the hierarchy of the graph shown in Fig. 1 resulting from application of the Strongly Connected Components algorithm.

Fig. 3. Hyper-structure analysis using the Strongly Connected Component algorithm. Four isolated components derived by the algorithm.


Fig. 4. Hierarchy corresponding to the structure in Fig. 3.


The rationale for employing this algorithm is that nodes should be strongly connected to each other if they belong to the same concept group. Using this algorithm allows us to identify which nodes cannot be reached from the starting node and whether the concept groupings accurately reflect the knowledge to be taught. Moreover, it guarantees that courseware authors will be able to derive sequences that place components in linear orders that can be used as recommended paths for students to follow through all the nodes in the courseware. As mentioned above, recommended paths can help students avoid becoming lost in hypermedia instructional systems, thereby allowing them to complete their reading processes more efficiently.

However, this algorithm is restricted in that it yields only two-level hypermedia hierarchies. Navigational maps based on such two-level structure are occasionally too shallow to cope with disorientation problems when the courseware is very large. Furthermore, although students can read every node in strongly connected components without backtracking, they must still go backward and forward to search for exit points to leave components. Consequently, the students may still have to repeat reading certain nodes within strongly connected courseware units. Under such circumstances, navigating through two-level maps provides a useful alternative for reaching other components.

C. Cut Vertex

The paths considered in the preceding analytical algorithms are important to this work. However, the fact that data are stored in nodes instead of on paths must also be considered. Below, we describe the Cut Vertex algorithm, which works on the nodes. A vertex (node) v is called a cut vertex of a graph if, after removal of node v, the graph has more components than the original graph. Thus, if a graph consists of exactly one component with a cut vertex v, then, by definition it will consist of at least two components after this node is removed. This means that students will miss much information in the courseware if they miss the cut vertex. Hence, courseware authors must be aware of whether cut vertices exist; if they do, they must be eliminated since they are weak points in connectivity.

On another hand, cut vertices can be used in a positive manner: they can be considered check points in the courseware, and quizzes can be assigned at such points so that students can confirm whether if they have satisfactorily comprehended the concepts presented in the preceding components. In such cases, the Cut Vertex algorithm can be used to confirm check points.

When using the Cut Vertex algorithm to analyze a courseware network, the cut vertices in the courseware network must initially be identified; they must then be removed from the courseware. After these nodes are removed, the courseware network then consists of several components that may be considered sub-topics of the courseware unit. The same graph algorithm can then be used to derive and remove cut vertices in these components. These steps are repeated until no cut vertex is present in any component. Fig. 5 and Fig. 6 show components and hierarchy, respectively.

Fig. 5. Hyper-structure analysis using the Cut Vertex algorithm. One cut vertex, E, is detected.


Fig. 6. Hierarchy corresponding to the structure in Fig. 5.


To utilize the three algorithms introduced above, analysts must first transform given sets of hypermedia nodes into directed graphs. This is achieved by employing any existing graph-traversal algorithm. For instance, one can start with one of the entry pages of the courseware. After representing the most recently visited courseware page as a graph node and giving it a name, one can explore all the pages reachable from the current page and construct links from the current page to the successive page. When no new nodes are left in the graph to explore, the procedure described above may be applied to the remaining pages until all pages have been represented. The resulting graph should be a connected one, or one in which some pages are inaccessible from the beginning. If the courseware homepage has a single entry point, every node should be reachable from it. After these initialization steps, one can implement the analytical algorithms to determine the soundness of the courseware structure.

When a minimal cut set is identified and the size of the set is small, it is possible that the two knowledge components have only a loose referential relationship to each other. This hypothesis can be verified by monitoring the actual navigation paths generated by students. If the traffic on these cut-set links is low, the concept groups are considered marginally relevant to each other. If that is not what the designer of the courseware expected, links should be added to strengthen the knowledge structure. When strongly connected components are identified, the designer should check to make sure that all nodes within the various groups are conceptually close to each other. Finally, when cut vertices are identified and they are not terminal nodes at branch ends, they should be studied with an eye toward setting check points. If one is not appropriate place for a check point, links should be added to eliminate its role as a cut vertex. On the other hand, if a desired check point is not found as a cut vertex that means unexpected by-pass routes exist in the structure. In any case, the designer is responsible for fixing the problems. 

III. Navigation in Educational Hypermedia

We work also examined how courseware structure influences the students' navigation. Below, we present two quantitative measures that show navigational behavior in terms of hyperness.

Sun & Ching [12] proposed a unit of measure for assessing the differences in navigation sequences in hyperspace. An algorithm called Longest Common Subsequences (LCS) was used to compute the lengths of common sub-sequences in strings. For instance, LCS may find the longest common sub-sequences "ABCBDAB" and "BDCABA", which are "BCBA" and "BDAB", both of length four. In other words, sub-sequences "BCBA" and "BDAB" can be found in both "ABCBDAB" and "BDCABA" in a similar, but not necessarily successive, ordering; and they are the longest of their kind. If we can identify long common sub-sequences between navigation paths, the navigators who produced the paths may employ similar strategies in exploring other sets of nodes. The LCS is thus used to represent similarities between sequences. If a linear visiting sequences exist, as provided by courseware designers or defined according to graph theory, plotting this measure against the standard sequence can be used to indicate how hyper (non-linear) a particular navigation path is.

Users can navigate in many ways in hypermedia environments without needing hotkeys. Thus, in this study, we introduce two more measures for evaluating students' navigational behaviors in hypermedia systems. The first, Hyper Degree, takes guidance tools into account indicating how hyper students' reading styles are. The second, Hyper Distance, employs base sequences to compute the lengths of students' average jumping distances from node to node.

A. Hyper Degree

As mentioned above, navigational tools constrain navigational styles. Using different navigation tools, e.g. hotkeys, bookmarks, or maps, may result in different navigation patterns. We next introduce the concept of candidate nodes, which are sets of nodes "linear-thinking" user are most likely to choose from. For instance, in typical educational hypermedia systems, students generally use three types of navigation tools: (1) hotkeys, (2) recommended paths, and (3) navigational maps. Thus, most likely candidate nodes for continuation can be defined in terms of these tools:

  1. Hotkeys: candidate nodes are the first hotkeys present in the students' current pages.
  2. Recommended paths: candidate nodes are those the recommended to visit next.
  3. Maps: candidate nodes are those nodes located next to current nodes on the maps.

We thus assign the highest degrees of linearity or the lowest degree of hyperness to students who always choose candidate nodes when reading. That is, when students select candidate nodes frequently, their navigation styles are considered relatively linear. Thus, we propose the following equation for computing hyper degree.

In the equation NCN denotes the number of candidate nodes selected, and LEN the length of an effective navigational path in number of nodes. When a student always follows candidate nodes, the number of candidate nodes followed equals the number of navigational actions. In this case, the student's Hyper Degree will be 0.

On the other hand, if his or her Hyper Degree is 1, the student's navigational pattern is considered extremely hyper. This measure provides a simple means of evaluating to what extent a student utilizes the cross-referencing facility provided by the hypermedia system.

B. Hyper Distance

Another means of defining the extent to which students navigate arbitrarily when given freedom of choice in hyper space is to compare their navigational sequences to systematic search sequences. Hyper Distance is thus defined as a measurement of the difference between base sequences and students' actual paths.

To calculate Hyper Distance, we initially arrange the courseware nodes by executing some search method, such as the Depth-First Search (DFS) or the Breadth-first Search (BFS) algorithm. DFS always expands one of the nodes at the current deepest level. Only when the search hits a dead end (no new nodes to explore from there) does the search go back and expand nodes at shallower levels. On the other hand, BFS expands the root node first, then all the nodes generated by the root node, and then their successors, and so on. See [13] for more details. Both algorithms provide systematic ways of exploring hypermedia nodes, thus either can be employed to generate base visiting sequences for purposes of comparison. Given a base sequence, we then order the nodes in this base sequence, and compute Hyper Distance according to this ordering. Hyper Distance is calculated as follows.

In this formula M denotes the total number of nodes visited, n(i) represents the position of node i in the base sequence, and N is the total number of navigation actions in the navigation process. The larger the actual distance between two nodes that are neighbors in the base sequence the larger the value of Hyper Distance yielded. If students follow visiting sequence identical to the base sequence, their Hyper Distances will be one, the minimal value. 

IV. Instructional Experiments

To validate the proposed methods, a courseware unit was selected and its structure analyzed. An instructional experiment was then performed using the CORAL system. In this experiment, we accumulated not only students' navigation activities but also their backgrounds and idiosyncrasies. The experiment was conducted in three stages. In the first stage, the students were given a pre-test to collect their idiosyncrasies and personal background information.

The second stage was the main part of this experiment in which students used the CORAL system to closely examine a hypermedia courseware lesson. In this stage, we assigned the subjects two tasks: browsing and searching. For the browsing task, the students were asked to read as many courseware nodes as possible. They could use any navigation tool and reading time was not constrained. For searching, on the other hand, we designed ten tasks, including looking for some text or graphic items in the courseware. Again, the students were free to use any navigation tool to search for the target nodes. The final stage was designed to determine the effects of students' learning using a post-test. In this study, we focused on the hyperness of the students' navigation patterns and the relationships between patterns and learning.

A. Courseware Structural Analysis

The courseware structure was analyzed by selecting a unit from previously developed Computer Network courseware. This courseware unit contained ninety-four nodes. Each node presented materials in multimedia such as text, graphics, and animation. Learning materials on specific topics were fitted into single screens to prevent users from having to use scroll bars, thus allowing them to concentrate fully on navigating through the hyper links.

We applied the three algorithms introduced above to analyze the courseware structure. According to those results, the courseware unit was well-structured, containing two strongly connected components with a clear conceptual boundary between the components. Our results further indicated that the students navigated through this courseware unit smoothly, without much backtracking. This courseware contained only a few cut vertices and they were all located at the ends of certain branches. Thus, students missing these nodes did not risk missing other nodes as well.

B. Navigational Behavior Analysis

We invited thirty-eight students majoring in literature and forty nine students registered in the teacher development program at the National Chiao Tung University to participate in this experiment. The students from the Literature department were freshman, and most of them did not know computer networks fundamentals. By contrast, the students in the teacher development program included undergraduate students and graduates who were more or less familiar with the computer network operations. Although differences in navigational patterns were expected due to students' diverse backgrounds, statistical analyses using SPSSX showed students' backgrounds did not correlate with our dependent measurements. Therefore, the data for all 87 students are reported collectively, with no distinctions made between groups.

All the navigation paths of the students were recorded. These records included what nodes were read, what navigation tools were used, and at what time a node was read. We used the Hyper Degree and the Hyper Distance measurements to analyze the navigational patterns of the subjects. Because the CORAL system contains more than ten navigation tools to assist reading, this study focused on the three most frequently used tools: (1) the recommended path, (2) the overview map, and (3) the hotkeys. Fig. 7 shows the students' Hyper Degree distribution. A normal distribution is found in the students' Hyper Degrees when they were allowed to use a combination of navigation tools. A normal distribution generally implies that the measure is a valid one since it can distinguish among samples along the given dimension.

Fig. 7. Distribution of hyper degree.

Hyper Distance is calculated on the basis of a reference sequence, and measures students' average jump distances. In this experiment, we employed the Depth First Search algorithm on the courseware to generate the reference sequence. Fig. 8 presents the students' Hyper Distance distribution. This figure also shows a normal distribution.

Fig. 8. Distribution of hyper distance.

An attempt was made to further confirm the usefulness of the measurements by identifying possible relationships between them and other variables. For instance, another study in the CORAL project focused on how learning styles and learning tasks influence the hypermedia learning environment. In that study, three learning styles were considered: Deep, Composite, and Shallow; learning tasks were also divided into two categories: Searching and Browsing.

No correlation was found between any two groups when Hyper Degree was used to measure the navigational patterns. However, a correlation was found when Hyper Distance was used, as shown in Table 1. The asterisks denote where correlations between two groups were identified.

Table 1. Correlation analysis based on hyper distance.

learning styles

















































V. Concluding Remarks

Students who navigate in hypermedia courseware enjoy convenience and flexibility. However, the problems of disorientation and cognitive overhead should be carefully addressed and properly remedied. An important feature of hypermedia environments is that they are dynamically updated in the sense that courseware nodes and the links between them are adjusted constantly. The new trend of collaborative courseware design and cross-referencing complicates matters even more. Consequently, the structure of courseware should be automatically demonstrated. In this study, we have presented novel techniques for constructing hierarchical structures to use in courseware analysis of educational hypermedia systems. The proposed approach has the following merits:

  1. Courseware authors can obtain useful information about how sound the courseware structure.
  2. The resulting information can be used in designing collaborative courseware and instructional strategies.
  3. Results from this study can be used directly as navigational maps to guide students in their reading processes.
  4. The proposed approach yields courseware with hierarchical concept maps, useful in assisting students to constructing knowledge.
  5. The pedagogical system can also provide a recommended path for navigation based on analysis.

While effective guidance tools can remedy the problem of disorientation, sound structure of hypermedia knowledge presentations are needed to alleviate cognitive overhead. For example, connecting only the most relevant materials in a strongly connected component should help conceptualization. Different navigation patterns may be attributable to different courseware structures. This work also proposes two methods for measuring the degree of linearity and hyperness to quantitatively characterize students' navigational patterns. Herein, we defined Hyper Degree and Hyper Distance. According to our pedagogical experiments, these measures provided further insights into students' learning behaviors. We hope results presented herein can help in developing systematic bases for constructing hypermedia courseware and analyzing navigational patterns.


The authors would like to thank the National Science Council, Taiwan, ROC, for financially supporting this research under Contract No. NSC85-2511-S-009-009-CL.


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Author Contact Information

Chuen-Tsai Sun, Associate Professor
Department of Computer and Information Science
National Chiao Tung University
Hsinchu, Taiwan
Phone: <+886 3-573-1972
Fax: <+886 3-572-1490

Chien Chou, Associate Professor
Institute of Communication Study
National Chiao Tung University
Hsinchu, Taiwan
Phone: <+886 3-573-1808

Bing-Kuen Lin
Department of Computer and Information Science
National Chiao Tung University
Hsinchu, Taiwan

Author Biographies

Chuen-Tsai Sun (S'90-M'93) is a Professor in the Department of Computer and Information Science at National Chiao Tung University in Taiwan, where he teaches courses in artificial intelligence, neural networks, evolutionary computing, and so on. He holds a Ph.D degree in Computer Science from University of California at Berkeley in 1992.

Chien Chou (M'95) is an Associate Professor in the Institute of Communication Studies at National Chiao Tung University in Taiwan, where she teaches courses in multimedia message design and evaluation, multimedia video, hypertext writing , and so on. She holds a Ph.D. degree in Instructional Design and Technology from The Ohio State University in 1990.

Bing-Kuen Lin received his B.S. degree in Department of Transportation Engineering and Management and M.S. degree in Computer and Information Science from National Chiao Tung University in 1994 and 1996 respectively. He is currently working as a System Analyst in Texas Instrument Taiwan Ltd. His research interests include hypertext structure, computer-assisted learning and so on.